Chapter 8.4, Problem 2E

To determine

To write: The quadratic equation that has a vertex of $\left(1,2\right)$.

Answer to Problem 2E

The quadratic equation with vertex $\left(1,2\right)$ is $y=2{\left(x-1\right)}^2+2$ (sample answer).

Explanation of Solution

Generally, the quadratic equation is the equation of the parabola.

The behavior of the graph of the parabola is U shaped curve where axis of symmetry can be drawn through the vertex of parabola.

The vertex form of the parabola is $a{\left(x-h\right)}^2+k$ where the point $\left(h,k\right)$ is the vertex.

Substitute $h=1\text{ and }k=2$ in the equation $a{\left(x-h\right)}^2+k$ to obtain quadratic equation.

  $y=a{\left(x-1\right)}^2+2$

Here, the value of $a$ can be any real number except 0.

Choose the value of $a=2$ to find a particular quadratic equation.

  $y=2{\left(x-1\right)}^2+2$

The quadratic equation $y=2{\left(x-1\right)}^2+2$ is the sample answer whose vertex is $\left(1,2\right)$ .